Ladder Operators and Dirac as the source.

TheShrike

Hello,

I've read that Dirac introduced the idea of the creation and annihilation operators in the solution to the quantum harmonic oscillator problem, but can anyone tell me where he did this? In a paper, or maybe in a book?

I've had a little search online, but I've yet to discover anything, so I thought I'd check the PF collective in case anyone knew off the top of their head.

andrien

you may try 'modern quantum mechanics' by sakurai.

Bill_K

The use of raising and lowering operators to solve the harmonic oscillator goes back at least as far as 1930, "Principles of Quantum Mechanics" by Dirac. See here, on p136.

dextercioby

Hi Bill, your link is to the 4th edition. One must provide us with the same page (if the same page) from the 1st edition of 1930.

Bill_K

Sorry, you're right. The best I can do is confirm that section 41 of the 1st edition is entitled "The Harmonic Oscillator", however the text of it does not seem to be available online.

( copies of the 1st edition sell for ~ $1500!)

dextercioby

Well, ita, itabar operators make sense only in the bra-ket context and there is no printed version of the bra-ket formalism before his 1930 book (?). Actually, I'm not sure which was the first textbook by another author copying Dirac's bra-ket treatment, but that of course after 1930, perhaps 1940.

TheShrike

Consensus seems to be that Dirac introduced them in his textbook on Quantum Mechanics. Ok, cool, thanks very much people.